With Jerry Sandusky set to be sentenced next month and Penn State fined $60 million by the NCAA, it might seem as though the embattled university can put the worst of this scandal behind it and start to rebuild. In fact, a new and potentially even more punitive phase is gearing up: the civil lawsuits by Sandusky’s victims. Three have already been filed — including “Victim One,” who testified at the Sandusky trail — and as many as 20 victims may ultimately sue.

There is a tendency to dismiss these kind of plaintiffs as opportunists looking for a big check. But we need lawsuits like these to put the heat on institutions that look the other way when bad things are happening. If the suits go to trial, juries will be asked to evaluate how much physical and emotional damage was done to the men (possibly a great deal) and how important it is to punish Penn State for its shocking failure to rein in the predator in its midst. A few hefty damage awards could send a powerful message not just to Penn State, but to other schools, corporations, and nonprofit organizations where abuse may be occurring.

Anyone whose job it is to balance an institution’s books should look with alarm on the prospect of a child sexual abuse lawsuits. In June, a Northern California jury awarded a woman $28 million — $7 million in compensatory damages, $21 million in punitive — against the Jehovah’s Witnesses for sexual abuse that she suffered as a child at the hands of a fellow congregant. The Sandusky victims could get awards of that size or perhaps even larger. If they have been traumatized for life by their abuse, the compensatory damages could be considerable, covering physical and emotional injuries and lost income.

Punitive damages could also be sizable given Penn State’s woeful response to red flags. University police knewas far back as 1998 that Sandusky had inappropriately touched a boy in the shower, but the football coach was not fired. Child welfare officials investigated Sandusky at the same time, but prosecutors did not bring criminal charges. Even when a university staff member — graduate assistant Mike McQueary — told superiors he had seen Sandusky raping a boy in the shower in 2002, the school failed to take decisive action. And if Tim Curley, the athletic director, and Gary Schultz, a former senior vice president, who are accused of lying to a grand jury about what McQueary told them and of failing to report the abuse, are convicted of perjury when they go to trial in January, the university may appear even more culpable in the eyes of a jury.

Under normal circumstances, Penn State might rely on its insurance company to pay the bills, but this is another source of vulnerability. The school’s general liability insurer, Pennsylvania Manufacturers’ Association Insurance, is arguing that the school withheld important information that it needed to assess risk and that its policies exclude coverage for sexual abuse. Penn State likely has enough money to handle whatever damages it might owe – with or without insurance – since its endowment stands at almost $2 billion, but still has cause to be worried about the financial hit: President Rodney Erickson told Bloomberg News last week that the school is working with lawyers to develop a process for settling “ideally all” of the suits.

For the victims, a settlement would mean they could avoid a trial and would get paid sooner. For Penn State, it would put a predictable cap on how much the school owes — and avoid another damaging round of publicity. For the nation, however, a few civil trials — and some eye-popping damage awards — might be a very good thing. One of the functions of the tort system, in addition to compensating victims, is imposing costs on things society wants to discourage. As the Penn State and Catholic Church scandals have made clear, the calculus for sexual abuse is out of whack. Top officials are still too inclined to look the other way when abuse charges are made and to circle the wagons when one of their own is accused.

It is hard to overcome these biases, but money can be a powerful countervailing force. Civil lawsuits can make people like Jerry Sandusky look less like eccentric colleagues and more like threats to an institution’s financial solvency. Reframing things in those dollars-and-cents terms should make it more likely that complaints of abuse will get the close attention they deserve.